Question #9f4fd

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Question #9f4fd

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Answer 1 · 2016-05-03T19:00:14

As a blended material:

$26 \frac{34}{41} %$ $26 34/41 %$ of the 1:10 material
$73 \frac{7}{41} %$ $73 7/41 %$ of the diluting material
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Or: add 30 more measures of the diluting material

Explanation:

$Preamble about ratios$ $color(blue)("Preamble about ratios")$

Consider the ratio of 1:10.

This consists of 1 part of something added to 10 parts of something else. So the total amount of parts is 11.

Thus a 1:10 ratio is a concentration of $\frac{1}{11} \times 100 = 9.09 ¯ ¯¯ ¯ 09 %$ $1/11xx100 = 9.09bar09%$

Where the bar means repeating for ever.

And 1:40 $\to \frac{1}{41} \times 100 \approx 2.439 %$ $-> 1/41xx100 ~~2.439%" "$ to 3 decimal places
.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Solving your question$ $color(blue)("Solving your question")$

You have a $1 : 10$ $1:10$ that you need to change to $1 : 40$ $1:40$

$Condition 1$ $color(blue)("Condition 1")$

$It does not matter that you have more volume/weight$ $color(brown)("It does not matter that you have more volume/weight")$

What ever you use to measure the 10 use to measure a further 30 giving you $1 : (10 + 30) \to 1 : 40$ $1:(10+30)->1:40$

$Condition 2$ $color(blue)("Condition 2")$
$You wish to blend the two so that have a specific volume/weight$ $color(brown)("You wish to blend the two so that have a specific volume/weight")$

$Some people do not like the following method but it works very well.$ $color(brown)("Some people do not like the following method but it works very well.")$

I use the principle of a straight line graph to plot the change in concentration as you gradually add more and more of one of the constituent. Thus able to determine the exact blend needed.

Tony B Tony B

The bottom axis measures the amount of diluting constituent from none at all to nothing but the diluting constituent.

$What follows is saying: the gradient of the little bit is the same all of it!$ $color(brown)("What follows is saying: the gradient of the little bit is the same all of it!")$
So we have: $x \div \frac{30}{451} = 100 \div \frac{1}{11}$ $" "x-:30/451=100-:1/11" "$

$x \times \frac{451}{30} = 100 \times \frac{11}{1}$ $" "x xx451/30=100xx11/1$

$x = \frac{100 \times 11 \times 30}{451}$ $" "x=(100xx11xx30)/(451)$

$x = 73 \frac{7}{41} %$ $x=73 7/41 %$ diluting material (exact value)

The amount of the original; 1:10 mixture is:

$100 - 73 \frac{7}{41} = 26 \frac{34}{41} %$ $100-73 7/41 = 26 34/41 %$ exact value
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check

$26 \frac{34}{41} \times \frac{1}{100} \times \frac{1}{11} = \frac{1}{41} This works so ok!$ $26 34/41 xx1/100xx 1/11 =1/41" "color(red)("This works so ok!")$

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Question #9f4fd

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